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SAN JOSE, California (CNN) -- The father of former NFL player Cpl. Pat Tillman said Monday he doesn't believe the full truth about his son's death in Afghanistan will ever emerge, despite a new investigation.

Tillman, who left the Arizona Cardinals for the Army after the 2001 al Qaeda attacks on New York and Washington, was killed by friendly fire in April 2004.

The Army, which originally reported that he died during a Taliban ambush, has now launched a criminal investigation to determine whether the death was the result of negligent homicide.

Pat Tillman Sr., a San Jose attorney, would not speak with CNN on camera. But he expressed frustration at the handling of his son's death so far and was pessimistic about the chances that the latest investigation would reveal anything new.

His son gave up a $3.6 million NFL contract to become an Army Ranger after the 9/11 attacks. He died in April 2004 in the mountains of southeastern Afghanistan as his unit battled remnants of the Taliban, the ultraconservative Islamic religious and political faction that had allowed al Qaeda to operate from its territory.

The Army initially reported that Tillman died fighting a Taliban ambush and posthumously awarded him the Silver Star, its third-highest combat decoration.

But a subsequent investigation revealed that fellow soldiers shot Tillman, thinking he was part of an enemy force firing at them -- and that top commanders had known almost immediately that his death was the result of friendly fire.

The Army apologized to Tillman's family in June. But last week, after looking into the previous investigations, the Pentagon's inspector general determined the Army never went through the process of conducting a criminal investigation.

Tillman's family has criticized previous Army investigations and demanded to know why his uniform and armor were burned a day after he was killed.

A 2005 report from Brig. Gen. Gary Jones contained sworn statements from soldiers involved in the incident who said they burned the items because they had taken pictures of the scene, walked around and knew how Tillman had been killed.

Initially, Tillman's blood-covered uniform and armor were said to have been destroyed because they were considered a biohazard.

Gen. Peter Pace, the chairman of the Joint Chiefs of Staff, said Sunday that it was "regrettable" the case was being reopened.